2001 Jeep Cherokee Alt/Battery problem

First off im no mechanic by any means but i putz on cars and i see you are looking for help. Clean your battery terminals (baking soda and water works well), then reconnect your battery. If that doesn't work I'd take that new battery back to where you bought it from and have it checked (even though its new). Whenever you install a new battery into a vehicle it should give you enough power to turn on things like courtesy lights, headlights, etc... and have at least enough power to turn the engine. When you leave cars sit for a long time things like starters and alternators can tighten up and not work well. Once you get it started again keep an eye on your alternator gauge, with a new battery in it should sit right in the middle - i believe it's 14 amps. If its not it could be your alternator or your battery cables, i have had to replace my cables on previous cars (positive typically will go to the starter and negative will go to your frame somewhere) and they can rust and break to the point that no current will travel through them (but then you shouldn't have been able to jump your jeep). Its probably your termanals or the new battery you just bought. Like i said I'm no professional, just another jeep owner hopefully this helps.

you could have a nasty short somewhere, check your positive cable and make sure there's no exposed wire grounding out on something.